I have been learning German for about a month now, and I am trying to understand the grammatical cases.
I read that we should say es tut mir leid to say I am sorry which I take to mean it makes me sorry. This confuses me; I thought that es is the subject and I (or ich) is the object. So, why do we not use the Accusative case for I, which is mich? Why do we use that dative mir?